@@ -2755,10 +2755,15 @@ def show(self):
         warning in `.Figure.show`.
         """
         # This should be overridden in GUI backends.
-        if cbook._get_running_interactive_framework() != "headless":
-            raise NonGuiException(
-                f"Matplotlib is currently using {get_backend()}, which is "
-                f"a non-GUI backend, so cannot show the figure.")
+        if sys.platform == "linux" and not os.environ.get("DISPLAY"):
+            # We cannot check _get_running_interactive_framework() ==
+            # "headless" because that would also suppress the warning when
+            # $DISPLAY exists but is invalid, which is more likely an error and
+            # thus warrants a warning.
+            return
+        raise NonGuiException(
+            f"Matplotlib is currently using {get_backend()}, which is a "
+            f"non-GUI backend, so cannot show the figure.")
 
     def destroy(self):
         pass
 
@@ -7,7 +7,6 @@
 import traceback
 
 import matplotlib
-
 from matplotlib import backend_tools, cbook
 from matplotlib._pylab_helpers import Gcf
 from matplotlib.backend_bases import (
@@ -108,15 +107,13 @@ def _create_qApp():
                     importlib.import_module(
                         # i.e. PyQt5.QtX11Extras or PySide2.QtX11Extras.
                         f"{QtWidgets.__package__}.QtX11Extras")
-                    is_x11_build = True
+                    x11_build = True
                 except ImportError:
-                    is_x11_build = False
+                    x11_build = False
             else:
-                is_x11_build = hasattr(QtGui, "QX11Info")
-            if is_x11_build:
-                display = os.environ.get('DISPLAY')
-                if display is None or not re.search(r':\d', display):
-                    raise RuntimeError('Invalid DISPLAY variable')
+                x11_build = hasattr(QtGui, "QX11Info")
+            if x11_build and matplotlib._c_internal_utils.display_is_invalid():
+                raise RuntimeError('Invalid DISPLAY variable')
 
             try:
                 QtWidgets.QApplication.setAttribute(
 
@@ -73,7 +73,8 @@ def _get_running_interactive_framework():
     if 'matplotlib.backends._macosx' in sys.modules:
         if sys.modules["matplotlib.backends._macosx"].event_loop_is_running():
             return "macosx"
-    if sys.platform.startswith("linux") and not os.environ.get("DISPLAY"):
+    if (sys.platform.startswith("linux")
+            and _c_internal_utils.display_is_invalid()):
         return "headless"
     return None
 
 
@@ -349,8 +349,10 @@ def get_extensions(self):
         # c_internal_utils
         ext = Extension(
             "matplotlib._c_internal_utils", ["src/_c_internal_utils.c"],
-            libraries=({"win32": ["ole32", "shell32", "user32"]}
-                       .get(sys.platform, [])))
+            libraries=({
+                "linux": ["dl"],
+                "win32": ["ole32", "shell32", "user32"],
+            }.get(sys.platform, [])))
         yield ext
         # contour
         ext = Extension(
 
@@ -1,11 +1,44 @@
 #define PY_SSIZE_T_CLEAN
 #include <Python.h>
+#ifdef __linux__
+#include <dlfcn.h>
+#endif
 #ifdef _WIN32
 #include <Objbase.h>
 #include <Shobjidl.h>
 #include <Windows.h>
 #endif
 
+static PyObject* mpl_display_is_invalid(PyObject* module)
+{
+#ifdef __linux__
+    void* libX11;
+    typedef struct Display Display;
+    Display* (* XOpenDisplay)(char* display_name);
+    int (* XCloseDisplay)(Display* display);
+    if (!(libX11 = dlopen("libX11.so", RTLD_LAZY)) ||
+        !(XOpenDisplay = dlsym(libX11, "XOpenDisplay")) ||
+        !(XCloseDisplay = dlsym(libX11, "XCloseDisplay"))) {
+        Py_RETURN_FALSE;
+    }
+    Display* display = XOpenDisplay(NULL);
+    if (display) {
+        XCloseDisplay(display);
+    }
+    if (dlclose(libX11)) {
+        PyErr_SetString(PyExc_RuntimeError, dlerror());
+        return NULL;
+    }
+    if (display) {
+        Py_RETURN_FALSE;
+    } else {
+        Py_RETURN_TRUE;
+    }
+#else
+    Py_RETURN_FALSE;
+#endif
+}
+
 static PyObject* mpl_GetCurrentProcessExplicitAppUserModelID(PyObject* module)
 {
 #ifdef _WIN32
@@ -66,6 +99,11 @@ static PyObject* mpl_SetForegroundWindow(PyObject* module, PyObject *arg)
 }
 
 static PyMethodDef functions[] = {
+    {"display_is_invalid", (PyCFunction)mpl_display_is_invalid, METH_NOARGS,
+     "display_is_invalid()\n--\n\n"
+     "Attempt to check whether the current X11 display is invalid.\n\n"
+     "Returns True if running on Linux and libX11 can be loaded and \n"
+     "XOpenDisplay(NULL) returns NULL, False otherwise."},
     {"Win32_GetCurrentProcessExplicitAppUserModelID",
      (PyCFunction)mpl_GetCurrentProcessExplicitAppUserModelID, METH_NOARGS,
      "Win32_GetCurrentProcessExplicitAppUserModelID()\n--\n\n"